445 lines
11 KiB
C++
445 lines
11 KiB
C++
/*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* Copyright 2011-2015 Danny Robson <danny@nerdcruft.net>
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*/
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#include "matrix.hpp"
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#include "debug.hpp"
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#include "iterator.hpp"
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#include "point.hpp"
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#include <cstring>
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#include <cmath>
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using namespace util;
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///////////////////////////////////////////////////////////////////////////////
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template <size_t S, typename T>
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matrix<S,T>
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matrix<S,T>::transposed (void) const
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{
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matrix<S,T> m;
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for (size_t i = 0; i < S; ++i)
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for (size_t j = 0; j < S; ++j)
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m.values[i][j] = values[j][i];
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return m;
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix<S,T>&
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matrix<S,T>::transpose (void)
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{
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for (size_t i = 0; i < S; ++i)
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for (size_t j = i + 1; j < S; ++j)
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std::swap (values[i][j], values[j][i]);
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return *this;
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix<S,T>&
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matrix<S,T>::invert (void)
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{
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return *this = inverse ();
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}
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//-----------------------------------------------------------------------------
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//template <size_t S, typename T>
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//matrix<S,T>&
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//matrix<S,T>::invert_affine (void)
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//{
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// CHECK (is_affine ());
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//
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// // inv ([ M b ] == [ inv(M) -inv(M).b ]
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// // [ 0 1 ]) [ 0 1 ]
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//
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// // Invert the 3x3 M
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// T A = (values[1][1] * values[2][2] - values[1][2] * values[2][1]);
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// T B = (values[1][2] * values[2][0] - values[1][0] * values[2][2]);
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// T C = (values[1][0] * values[2][1] - values[1][1] * values[2][0]);
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//
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// T D = (values[0][2] * values[2][1] - values[0][1] * values[2][2]);
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// T E = (values[0][0] * values[2][2] - values[0][2] * values[2][0]);
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// T F = (values[2][0] * values[0][1] - values[0][0] * values[2][1]);
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//
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// T G = (values[0][1] * values[1][2] - values[0][2] * values[1][1]);
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// T H = (values[0][2] * values[1][0] - values[0][0] * values[1][2]);
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// T K = (values[0][0] * values[1][1] - values[0][1] * values[1][0]);
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//
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// T d = values[0][0] * A + values[0][1] * B + values[0][2] * C;
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// CHECK_NEQ (d, 0.0);
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//
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// values[0][0] = A / d;
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// values[0][1] = D / d;
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// values[0][2] = G / d;
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// values[1][0] = B / d;
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// values[1][1] = E / d;
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// values[1][2] = H / d;
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// values[2][0] = C / d;
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// values[2][1] = F / d;
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// values[2][2] = K / d;
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//
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// // Multiply the b
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// T b0 = - values[0][0] * values[0][3] - values[0][1] * values[1][3] - values[0][2] * values[2][3];
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// T b1 = - values[1][0] * values[0][3] - values[1][1] * values[1][3] - values[1][2] * values[2][3];
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// T b2 = - values[2][0] * values[0][3] - values[2][1] * values[1][3] - values[2][2] * values[2][3];
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//
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// values[0][3] = b0;
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// values[1][3] = b1;
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// values[2][3] = b2;
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//
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// return *this;
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//}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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T
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util::matrix<S,T>::determinant (void) const
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{
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return util::determinant (*this);
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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util::matrix<S,T>
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util::matrix<S,T>::inverse (void) const
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{
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return util::inverse (*this);
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}
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///////////////////////////////////////////////////////////////////////////////
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template <size_t S, typename T>
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matrix<S,T>
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util::transposed (const matrix<S,T> &m)
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{
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util::matrix<S,T> res;
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for (size_t y = 0; y < S; ++y)
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for (size_t x = 0; x < S; ++x)
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res[y][x] = m[x][y];
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return res;
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}
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///////////////////////////////////////////////////////////////////////////////
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template <size_t S, typename T>
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matrix<S,T>
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matrix<S,T>::operator* (const matrix<S,T> &rhs) const
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{
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matrix<S,T> m;
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for (unsigned row = 0; row < S; ++row) {
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for (unsigned col = 0; col < S; ++col) {
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m.values[row][col] = T {0};
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for (unsigned inner = 0; inner < S; ++inner)
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m.values[row][col] += values[row][inner] * rhs.values[inner][col];
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}
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}
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return m;
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix<S,T>&
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matrix<S,T>::operator*=(const matrix<S,T> &rhs)
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{
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return *this = *this * rhs;
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}
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///////////////////////////////////////////////////////////////////////////////
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template <size_t S, typename T>
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vector<S,T>
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matrix<S,T>::operator* (const vector<S,T> &rhs) const
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{
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vector<S,T> out;
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for (size_t i = 0; i < S; ++i)
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out[i] = dot (rhs, values[i]);
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return out;
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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point<S,T>
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matrix<S,T>::operator* (const point<S,T> &rhs) const
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{
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point<S,T> out;
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for (size_t i = 0; i < S; ++i)
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out[i] = dot (rhs, values[i]);
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return out;
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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bool
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matrix<S,T>::is_affine (void) const
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{
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for (size_t i = 0; i < S - 1; ++i)
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if (!exactly_zero (values[S-1][i]))
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return false;
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return exactly_equal (values[S-1][S-1], T{1});
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::ortho (T left, T right,
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T bottom, T top,
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T near, T far)
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{
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CHECK_GT (far, near);
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T tx = - (right + left) / (right - left);
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T ty = - (top + bottom) / (top - bottom);
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T tz = - (far + near) / (far - near);
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T rl = 2 / (right - left);
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T tb = 2 / (top - bottom);
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T fn = 2 / (far - near);
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return { {
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{ rl, 0, 0, tx },
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{ 0, tb, 0, ty },
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{ 0, 0, fn, tz },
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{ 0, 0, 0, 1 },
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} };
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::ortho2D (T left, T right,
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T bottom, T top)
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{
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return ortho (left, right, bottom, top, -1, 1);
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::perspective (T fov, T aspect, range<T> Z)
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{
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T f = std::tan (fov / 2);
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T tx = 1 / (f * aspect);
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T ty = 1 / f;
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T z1 = (Z.max + Z.min) / (Z.min - Z.max);
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T z2 = (2 * Z.max * Z.min) / (Z.min - Z.max);
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return { {
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{ tx, 0, 0, 0 },
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{ 0, ty, 0, 0 },
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{ 0, 0, z1, z2 },
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{ 0, 0, -1, 0 }
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} };
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}
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//-----------------------------------------------------------------------------
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// Emulates gluLookAt
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::look_at (util::point<3,T> eye,
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util::point<3,T> target,
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util::vector<3,T> up)
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{
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const auto f = normalised (target - eye);
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const auto s = normalised (cross (f, up));
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const auto u = cross (s, f);
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return { {
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{ s.x, s.y, s.z, -dot (s, eye) },
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{ u.x, u.y, u.z, -dot (u, eye) },
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{ -f.x, -f.y, -f.z, dot (f, eye) },
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{ 0, 0, 0, 1 },
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} };
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::translation (util::vector<2,T> v)
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{
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return translation ({v.x, v.y, 0});
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::translation (util::vector<3,T> v)
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{
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return { {
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{ 1.f, 0.f, 0.f, v.x },
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{ 0.f, 1.f, 0.f, v.y },
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{ 0.f, 0.f, 1.f, v.z },
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{ 0.f, 0.f, 0.f, 1.f },
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} };
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::scale (T mag)
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{
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return scale (vector<3,T> (mag));
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::scale (util::vector<3,T> v)
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{
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return { {
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{ v.x, 0.f, 0.f, 0.f },
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{ 0.f, v.y, 0.f, 0.f },
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{ 0.f, 0.f, v.z, 0.f },
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{ 0.f, 0.f, 0.f, 1.f }
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} };
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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matrix4<T>
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matrix<S,T>::rotation (T angle, util::vector<3,T> about)
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{
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CHECK (is_normalised (about));
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T c = std::cos (angle);
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T s = std::sin (angle);
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T x = about.x,
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y = about.y,
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z = about.z;
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return { {
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{ x * x * (1 - c) + c,
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x * y * (1 - c) - z * s,
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x * z * (1 - c) + y * s,
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0
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},
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{ y * x * (1 - c) + z * s,
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y * y * (1 - c) + c,
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y * z * (1 - c) - x * s,
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0
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},
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{ z * x * (1 - c) - y * s,
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z * y * (1 - c) + x * s,
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z * z * (1 - c) + c,
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0
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},
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{ 0, 0, 0, 1 }
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} };
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}
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//-----------------------------------------------------------------------------
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template <size_t S, typename T>
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const matrix<S,T>
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matrix<S,T>::ZEROES { 0 };
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//-----------------------------------------------------------------------------
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template struct util::matrix<2,float>;
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template struct util::matrix<2,double>;
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template struct util::matrix<3,float>;
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template struct util::matrix<3,double>;
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template struct util::matrix<4,float>;
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template struct util::matrix<4,double>;
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///////////////////////////////////////////////////////////////////////////////
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// Uses the algorithm from:
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// "Extracting Euler Angles from a Rotation Matrix" by
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// Mike Day, Insomniac Games.
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template <size_t S, typename T>
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util::vector<3,T>
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util::to_euler (const matrix<S,T> &m)
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{
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static_assert (S == 3 || S == 4, "only defined for 3d affine transforms");
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const auto theta0 = std::atan2 (m[2][1], m[2][2]);
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const auto c1 = std::hypot (m[0][0], m[1][0]);
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const auto theta1 = std::atan2 (-m[2][0], c1);
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const auto s0 = std::sin(theta0);
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const auto c0 = std::cos(theta0);
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const auto theta2 = std::atan2(
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s0 * m[0][2] - c0 * m[0][1],
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c0 * m[1][1] - s0 * m[1][2]
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);
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return { theta0, theta1, theta2 };
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}
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//-----------------------------------------------------------------------------
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template util::vector<3,float> util::to_euler (const matrix<3,float>&);
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template util::vector<3,float> util::to_euler (const matrix<4,float>&);
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///////////////////////////////////////////////////////////////////////////////
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template <size_t S, typename T>
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std::ostream&
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util::operator<< (std::ostream &os, const matrix<S,T> &m)
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{
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os << "{ ";
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for (size_t i = 0; i < S; ++i) {
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os << "{ ";
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std::copy (m[i], m[i]+S, util::infix_iterator<float> (os, ", "));
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os << ((i == S - 1) ? " }" : " }, ");
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}
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return os << " }";
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}
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//-----------------------------------------------------------------------------
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template std::ostream& util::operator<< (std::ostream&, const matrix<4,float>&);
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template std::ostream& util::operator<< (std::ostream&, const matrix<4,double>&);
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